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<span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <br/> for <font color="Olive" title="b2">a</font> being  <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Olive" title="b2">a</font> &amp; <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>(  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Olive" title="b1">a</font> &amp; <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>(  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies (  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:99"/><span class="lab"><font color="Green" title="E66">A1</font></span>: 
<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c6">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or (  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:99"/><span class="lab"><font color="Green" title="E67">A2</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:99_1"/>
( <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c6">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c6">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1"><span class="kw">suppose </span></a><a NAME="E1:99_1_1"/><span class="lab"><font color="Green" title="E68">A3</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c6">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> )</span><br/><div class="add"><a NAME="E2:99_1_1"/>
 <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> <font color="Maroon" title="c6">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> <font color="Maroon" title="c6">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T63" title="SCMFSA6A:th.63">SCMFSA6A:63</a></span>;<br/><a NAME="E3:99_1_1"/><span class="kw">then </span>
 <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">I</font> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> <font color="Maroon" title="c6">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99"><span class="lab"><font color="Green" title="E66">A1</font></span></a>, <a class="txt" href="#E2:99"><span class="lab"><font color="Green" title="E67">A2</font></span></a>, <a class="txt" href="#E1:99_1_1"><span class="lab"><font color="Green" title="E68">A3</font></span></a>, <a class="ref" href="scm_halt.html#T73" target="_self" title="SCM_HALT:th.73">Th73</a></span>;<br/><span class="kw">hence </span><a NAME="E4:99_1_1"/>
(  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1_1"><span class="lab"><font color="Green" title="E68">A3</font></span></a>, <a class="ref" href="scmfsa8c.html#T68" title="SCMFSA8C:th.68">SCMFSA8C:68</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_2"><span class="kw">suppose </span></a><a NAME="E1:99_1_2"/><span class="lab"><font color="Green" title="E68">A4</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c6">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> )</span><br/><div class="add"><a NAME="E2:99_1_2"/>
(  <a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmnorm.html#K2" title="SCMNORM:func.2">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T24" title="SCMFSA7B:th.24">SCMFSA7B:24</a>, <a class="ref" href="scmfsa7b.html#T25" title="SCMFSA7B:th.25">SCMFSA7B:25</a></span>;<br/><span class="kw">hence </span><a NAME="E3:99_1_2"/>
(  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="scmfsa8c.html#K2" title="SCMFSA8C:func.2">Times</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1_2"><span class="lab"><font color="Green" title="E68">A4</font></span></a>, <a class="ref" href="scmfsa8b.html#T24" title="SCMFSA8B:th.24">SCMFSA8B:24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
